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Each checkpoint condition is translated into a group of specific sequences of state transitions that can be derived by ordering pairs of state transition among Clb2, Cdc20 and their interacting genes.
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These hybrid carrier components can be derived by different order 4-WFRFT transform.
The formula can also be derived by the time ordered product expansion described in [ 55] without resorting to time discretization, as shown below.
The self-consistent-charge density functional tight-binding (SCC-DFTB), which can be derived by a second order expansion of the DFT total energy, extends the DFTB methods to charge self-consistency.
The equation of the state sensitivity matrix can be derived by taking the first order partial derivative of Eq. (1) with respect to parameters p (3) S ˙ = ∂ f ∂ x S + ∂ f ∂ p where S = ∂ x ∂ p is the state sensitivity matrix.
In the present study some recursive relations have been implemented which can be derived by using the first order central differences and application of these simple and elegant relations to higher order difference schemes has been demonstrated to improve the accuracy over conventional approaches.
Household's demand for food C f can be derived by solving the first-order conditions of the RHS of Eq. 10.
The estimation method of Newton Raphson employed in this research can be derived by taking the second order Taylor's approximation of LL(β t + 1) around LL(β t ) and the details are as follows.
The demand for inputs and output produced, especially for households that produced their food at home, can be derived by maximizing the first-order condition of the LHS of Eq. 10 with respect to labour (L) and output produced (Q) as: {L}^={l}^left {P}_{hp}, w,{A}^0,{K}^0right) (11) {Q}^={Q}_{hp}^left {P}_{hp}, w,{A}^0,{A}^0right) (12).
Then the reduced order model can be derived by truncating the balanced model.
Because the first derivative of the arterial pulse waveform denotes the moving velocity of the arterial wall, the maximum velocity point can be derived by finding the peak of the first-order differential curve of the arterial pulse waveform (4(b)).
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